Method and system for determining a color formula

Abstract

The invention relates to a method to determine a formula for a sample color matching a target color, based on an obsolete color formula, based on a given range of tinting bases. According to the proposed method, a color prediction model is used to calculate a distance between respective color parameters of a candidate color formula and the color parameters of the target color, and a genetic algorithm is used to obtain the formula for the sample color out of a population of candidate color formulas, wherein a distance of respective color parameters of a candidate color formula of the population of candidate color formulas to the color parameters of the target color is minimized by the genetic algorithm by iterative steps of mutation/crossing-over and selection of candidate color formulas that fit best to a fitness criterion, until a pre-given stopping criterion is fulfilled which automatically leads to a candidate color formula which is kept as the sample color formula.

1 . A method to determine a formula for a sample color matching a target color, based on an obsolete color formula, based on a given range of tinting bases, the method comprising:
 a) determining at least one intrinsic feature of the obsolete color formula based on at least one physical property of the target color;   b) linking the at least one determined intrinsic feature of the obsolete color formula via a mathematical model to defined color parameters of a color prediction model, thus obtaining color parameters of the target color, the color prediction model being set up based on a given database between color parameters and formula intrinsic features and the mathematical model;   c) using the color prediction model to calculate a distance between respective color parameters of a candidate color formula and the color parameters of the target color;   d) using a genetic algorithm to obtain the formula for the sample color out of a population of candidate color formulas by repeating c), wherein a distance of respective color parameters of a candidate color formula of the population of candidate color formulas to the color parameters of the target color is minimized by the genetic algorithm by iteration of mutation/crossing-over and selection of candidate color formulas that fit best to a fitness criterion, until a pre-given stopping criterion is fulfilled which automatically leads to a candidate color formula which is kept as the sample color formula.   
     
     
         2 . The method according to  claim 1 , wherein the population of candidate color formulas is generated randomly. 
     
     
         3 . The method according to  claim 1 , wherein the population of candidate color formulas is generated with respect to provided expert knowledge. 
     
     
         4 . The method according to  claim 1 , wherein the stopping criterion is given by a distance threshold wherein, if respective color parameters of a candidate color formula are closer to the color parameters of the target color than the distance threshold, the corresponding candidate color formula is kept as the sample color formula. 
     
     
         5 . The method according to  claim 1 , wherein the stopping criterion is given by a settled maximum number of iterations such that, if after this number of iterations none of the candidate color formulas has a distance below a pre-defined distance threshold, the candidate color formula with the smallest distance is kept as the sample color formula. 
     
     
         6 . The method according to  claim 1 , wherein the mathematical model is based on a Kubelka-Munk two flux model. 
     
     
         7 . The method according to  claim 1 , wherein a statistical method is applied to the database linking color parameters and color formulas, thus serving as the color prediction model. 
     
     
         8 . The method according to  claim 7  wherein the statistical method is at least one selected from the group consisting of linear regression, PLS regression, supervised learning methods and k-nearest neighbors. 
     
     
         9 . The method according to  claim 1 , wherein a scattering coefficient and/or an absorption coefficient are chosen as the at least one intrinsic feature of the target color. 
     
     
         10 . The method according to  claim 9 , wherein any combination or calculation based on the scattering coefficient and/or the absorption coefficient can be considered as the at least one intrinsic feature of the target color. 
     
     
         11 . The method according to  claim 1 , wherein reflectance curve values measured by a spectrocolorimeter are used as color parameters. 
     
     
         12 . The method according to  claim 1 , wherein each candidate color formula of the population of candidate color formulas derived by the genetic algorithm is evaluated by the distance of its color parameters to the color parameters of the obsolete color formula through the color prediction model. 
     
     
         13 . The method according to  claim 12 , wherein the evaluation is iterated n-times. 
     
     
         14 . A computer program for performing a method according to  claim 1 , wherein the computer program is stored on a computer-readable medium. 
     
     
         15 . A color matching system for determining a sample color formula, wherein the system comprises at least a calculation device for providing a color prediction model and a genetic algorithm as used by the method according to  claim 1 . 
     
     
         16 . The method according to  claim 1 , further comprising:
 e) preparing a paint whose color matches the target color, based on the sample color formula obtained in d).